(ie. the plugin is installed locally. If you want to install it globally - which is not recommended - check out the official grunt documentation)

You also need to install the temporary module

Although it is marked as a dependency in the grunt-jasmine-task module and automatically is installed together with the jasmine plugin, for some reason it cannot be found, therefore it needs to be installed separately, either as a global or local module.

To install it locally do:
npm install temporary

Then add this line to your project's grunt.js gruntfile at the bottom:

grunt.loadNpmTasks('grunt-jasmine-task');

Next you need to create (a) target(s) for the jasmine task.

If you want to run one file just add this to the grunt.initConfig object

jasmine: {
all: ['specs/specrunner.html']
},

Obviously you need to replace specs/specrunner.html with the location of your jasmine spec running html file.

This is useful for async assertions that may require more than 10 seconds to run.

Now you can run the jasmine task with:

grunt jasmine

When specs fail...

By default the jasmine task outputs in non-verbose mode, meaning it will output dots for passed specs and F's for failed ones.
You can see which spec is failing by running the task in verbose mode:grunt jasmine -v
or (since v0.2.1) you can turn on reporting for failing specs even in non-verbose mode, see errorReporting config option

Contributing

In lieu of a formal styleguide, take care to maintain the existing coding style.
Add unit tests for any new or changed functionality.
Lint and test your code using grunt.